Electrical capacitance tomography (ECT) is a technique to determine the dielectric permittivity distribution in the interior of an object from external capacitance measurements. ECT's advantages over conventional tomographic techniques include non-intrusiveness, non-destruction, no radiation hazard, and low cost. In industry, ECT has found many applications, such as measurement of gas/liquid and gas/solid flows in pipelines; analysis of dynamic processes in fluidized beds; monitoring of mixing and separation processes; visualization of combustion flames in engine cylinders; and detection of leakage from buried water pipes.
ECT enables insight into the material distribution within a closed vessel, and consequently, into the governing mechanism in processes occurring within the vessel, without disturbing the processes themselves. Research on ECT encompasses sensor design, capacitance measuring circuit design, and image reconstruction. While sensor and circuit design involve hardware, image reconstruction typically involves software.
FIG. 1 shows a typical ECT system 100 that includes the following components: (1) an ECT sensor 110 that registers physical responses from the object being measured; (2) excitation and measurement circuitry 120 that drives the sensor 110 and conditions the received signals; and (3) a computer-based data acquisition and channel switching system 130 to provide control signals 134 for the sequential excitation of the electrodes. The computer-based system 130 can also reconstruct tomographic images of the object based on the measured data 132.
As shown in FIG. 1, the ECT sensor 110 consists of a total of M electrodes 111a-111m that are mounted symmetrically outside of a cylindrical container 114. Traditionally, during each scanning frame, an excitation signal in the form of an alternating current (AC) voltage is applied to one of the electrodes, e.g., electrode 111a, and the remaining electrodes 111b-111m are kept at ground potential to act as detector electrodes. Subsequently, the voltage potential at each of the remaining electrodes 111b-111m is measured, one at a time, by the measurement electronics 120 to determine the inter-electrode capacitance. Specifically, in the first round of the measurements, inter-electrode capacitance is measured between electrodes 111a and 111b. Next, capacitance is measured between electrodes 111a and 111c, then between electrode 111a and 111d, and so on. In the second round of measurements, the capacitances is measured first between electrodes 111b and 111c, then between electrodes 111b and 111d, and so on. Measurement cycles continue with each individual electrode assuming the role of an excitation source and a detector, alternately, until all the inter-electrode capacitances are measured.
The measured capacitances can be then represented in a matrix and used to reconstruct the tomographic image of the object within the cylindrical container. Analytically, with M electrodes 111a-111m in the ECT sensor 110, a total number of H independent capacitance measurements take place, where H=M(M−1)/2. In ECT systems reported in the literature, the number of electrodes M was typically chosen to be 6, 8, 12, 16, and 32. Thus, the number of independent capacitance measurements H was 15, 28, 66, 120, and 496, respectively.
The number of capacitance measurements to be performed by the ECT sensor is a parameter that affects the quality of the reconstructed image. Increasing the number of electrodes improves the resolution of the reconstructed image. For a given measurement area, however, increasing the number of electrodes also causes each electrode to have a smaller surface, thus decreasing the magnitude of the inter-electrode capacitance, which, in turn, leads to a lower signal-to-noise ratio (SNR) given fixed background noise.
One solution to this problem is the grouping technique, which involves combining two or more electrodes into one segment to increase the magnitude of the received signal, as shown in FIG. 2. However, excitation of the electrodes within each segment is still performed in steps of one electrode at a time only. This grouping configuration is repeated along the sensor circumference by shifting the connection by one electrode in each measurement to form a series of independent measurements.
FIG. 2 shows an eight-electrode sensor 110 operated in the four-segment mode. The total surface area covered by electrodes 111a-111m equals that of a four-electrode ECT sensor without segmentation, so the SNR remains the same as that of the four-segment sensor. After measuring the first six capacitance values for a first configuration 202, the electrodes 111a-111m are re-connected in a second configuration 204. This can be viewed as a rotation of the four electrodes by θ=45°. As a result, the total number of independent measurements performed by the ECT electronics in each scanning frame is twice as high (twelve vs. six) compared to a conventional four-electrode sensor, thus achieving higher resolution for better image reconstruction.
Scanning speed is an important parameter of an ECT system, as it determines the usability of ECT for on-line, real-time applications involving fast changing dynamics, such as combustion or explosion within an enclosure. Currently, the maximum scanning speed achieved by ECT is about 300-1,000 frames/second. While satisfactory for general applications, this speed is far lower than what can be achieved with optical methods, although optical methods need direct access to the process to be monitored and thus are subject to various constraints (e.g., blockage of the line of sight) in real-world environments. For engine combustion process imaging, which is not easily monitored using optical methods, it is desirable to resolve the process at every crank angle (i.e., in 1° increments) at crank rotational speeds of up to 6,000 rev/min. This requires an ECT system that can collect data at a speed of up to 36,000 frames/second.